Question: Solve for $x$ and $y$ using elimination. ${3x+2y = 17}$ ${-x+3y = 20}$
Solution: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the bottom equation by $3$ ${3x+2y = 17}$ $-3x+9y = 60$ Add the top and bottom equations together. $11y = 77$ $\dfrac{11y}{{11}} = \dfrac{77}{{11}}$ ${y = 7}$ Now that you know ${y = 7}$ , plug it back into $\thinspace {3x+2y = 17}\thinspace$ to find $x$ ${3x + 2}{(7)}{= 17}$ $3x+14 = 17$ $3x+14{-14} = 17{-14}$ $3x = 3$ $\dfrac{3x}{{3}} = \dfrac{3}{{3}}$ ${x = 1}$ You can also plug ${y = 7}$ into $\thinspace {-x+3y = 20}\thinspace$ and get the same answer for $x$ : ${-x + 3}{(7)}{= 20}$ ${x = 1}$